O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2012 · Q24 Marks
The total surface area, A cm², of a solid cylinder with radius r cm and height 5 cm is given by A = 2πr² + 10πr. Given that r is increasing at a rate of 0.2 cms⁻¹, find the rate of increase of A when r is 6.
- The total surface area, A cm², of a solid cylinder with radius r cm and height 5 cm is given by A = 2πr² + 10πr. Given that r is increasing at a rate of 0.2 cms⁻¹, find the rate of increase of A when r is 6.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.
- [B1,B1] (dA/dr =) 4πr + 10π
- [M1] Use dA/dt = dA/dr × dr/dt with r = 6
- [A1] 6.8
- [A1] Rounds to 6.8
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